It is known that the complementarity problems and the variational inequality problems are reformulated equivalently as a vector equation by using the natural residual or Fischer-Burmeister function. In this short paper, we first study the global convergence of a sequential injective algorithm for weakly univalent vector equation. Then, we apply the convergence analysis to the regularized smooth...

Quantitative estimates are obtained for the (finite) valence of functions analytic in the unit disk with Schwarzian derivative that is bounded or of slow growth. A harmonic mapping is shown to be uniformly locally univalent with respect to the hyperbolic metric if and only if it has finite Schwarzian norm, thus generalizing a result of B. Schwarz for analytic functions. A numerical bound is obt...

let $omega_x$ be a bounded, circular and strictly convex domain of a banach space $x$ and $mathcal{h}(omega_x)$ denote the space of all holomorphic functions defined on $omega_x$. the growth space $mathcal{a}^omega(omega_x)$ is the space of all $finmathcal{h}(omega_x)$ for which $$|f(x)|leqslant c omega(r_{omega_x}(x)),quad xin omega_x,$$ for some constant $c>0$, whenever $r_{omega_x}$ is the m...

Let f(z) be any transcendental entire function. Let r, denote the absolute value of the zero z. of f '(z) which is nearest to the origin. Alander, Erdö's and Renyi, and Polya have investigated the relation between r, and the growth of the function /(z). Let s, denote the ... fz largest disk about the origin where / (z) is univalent. Boas, Levinson, and Polya have obtained some relations between...

In this manuscript, we introduce concepts of (m1,m2)-logarithmically convex (AG-convex) functions and establish some Hermite-Hadamard type inequalities of these classes of functions.

A continuous function f u iv is a complex-valued harmonic function in a simply connected complex domain D ⊂ C if both u and v are real harmonic in D. It was shown by Clunie and Sheil-Small 1 that such harmonic function can be represented by f h g, where h and g are analytic in D. Also, a necessary and sufficient condition for f to be locally univalent and sense preserving in D is that |h′ z | >...

License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We consider meromorphic starlike univalent functions that are also bi-starlike and find Faber polynomial coefficient estimates for these types of functions. A function is said to be bi-starlike if both the function and its inverse are starlike univalent. Consider ...